Question #056a7

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Answer 1 · 2017-11-05T18:04:33

#sec^2(x)#

Rewrite the expression: #1+tanx=1+sinx/cosx#

=#d/dx (1+sinx/cosx)#

differentiate the sum term by term

= #d/dx(1)+d/dx(sinx/cosx)#

the derivative of 1 is zero

#d/dx(sinx/cosx)#

Use the quitient rule

#(d/dx((sinx))cosx-(d/dx(cosx)sinx))/(cos^(x))#

simplify

#(cos^2(x)+sin^2(x))/(cos^2(x)#

use the Pythagorean identity #cos^2(x)+sin^2(x)=1#

#=(1/cos^2(x))#

#=sec^2(x)#